What is the RiskFree Rate Formula?
A riskfree rate of return formula calculates the interest rate that investors expect to earn on an investment that carries zero risks, especially default risk and reinvestment risk, over some time. It is usually closer to the base rate of a Central Bank and may differ for the different investors. It is the rate of interest offered on sovereign or government bonds or the bank rate set by the country’s Central Bank. These rates are the function of many factors like â€“ Rate of Inflation formulaRate Of Inflation FormulaThe rate of inflation formula helps understand how much the price of goods and services in an economy has increased in a year. It is calculated by dividing the difference between two Consumer Price Indexes(CPI) by previous CPI and multiplying it by 100.read more, GDP Growth rate, foreign exchange rate, economy, etc.
The riskfree rate of returnRiskfree Rate Of ReturnA riskfree rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of welldeveloped countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more is a key input in arriving at the cost of capitalCost Of CapitalThe cost of capital formula calculates the weighted average costs of raising funds from the debt and equity holders and is the total of three separate calculations â€“ weightage of debt multiplied by the cost of debt, weightage of preference shares multiplied by the cost of preference shares, and weightage of equity multiplied by the cost of equity.read more and hence is used in the capital asset pricing modelCapital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more. This model estimates the required rate of return on investment and how risky the investment is compared to the total riskfree asset. It is used in the calculation of the cost of equityCalculation Of The Cost Of EquityCost of Equity (Ke) is what shareholders expect for investing their equity into the firm. Cost of equity = Risk free rate of return + Beta * (market rate of return  risk free rate of return). read more, which influences the companyâ€™s WACC.
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Key Takeaways
 Riskfree rate of return formula calculates investors’ expected interest rate on zerorisk investments, typically closer to a Central Bank’s base rate. It depends on factors like inflation, GDP growth, foreign exchange rate, and economy.
 The riskfree rate of return is crucial for estimating capital cost, influencing asset price models, and calculating the cost of equity, impacting a company’s WACC.
 Investors gain from an increased riskfree rate of return since it shows that the government is stable and confident. Companies may face pressure to boost stock prices to meet investors’ expectations for increased profits.
Below is the formula to derive the Cost of Equity using the riskfree rate of return using the model :
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CAPM Model
Frequently Asked Questions (FAQs)
Additionally crucial for determining the Sharpe ratio is the riskfree rate. The riskadjusted returns on a single security or an entire investment portfolio are assessed using this analytical method. The better the investment, the greater the ratio for both the CAPM and the Sharpe ratio.
The market’s riskfree rate plus a premium for the investment’s inherent risk determine the cost of capital. If investors were risk averse, the riskfree rate would be the proper discount rate for calculating the present value of projected net cash flows.
Any return over the riskfree rate is considered a risk premium. The rate of return on an item or investment that, theoretically, carries no risk, such as a government bond, is the riskfree rate.
where,
 Re: Cost of Equity
 Rf: Riskfree rate
 Rm: Market Risk PremiumMarket Risk PremiumThe market risk premium is the supplementary return on the portfolio because of the additional risk involved in the portfolio; essentially, the market risk premium is the premium return investors should have to make sure to invest in stock instead of riskfree securities.read more
 RmRf: Expected ReturnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + â€¦â€¦â€¦â€¦ + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more
However, It is usually the rate at which the government bonds and securities are available and inflationadjusted. The following formula shows how to arrive at the riskfree rate of return:
This riskfree rate should be inflationadjusted.
Explanation of the Formula
The various applications of the riskfree rate use the cash flows in real terms. Hence, the riskfree rate must also be brought to the same real terms, which is inflationadjusted for the economy. Since the rate is mostly the longterm government bonds â€“ they are adjusted to the rate of inflation factor and provided for further use.
The calculation depends upon the time period in evaluation.
 If the period is up to 1 year, one should use the most comparable government security, which is the Treasury BillsTreasury BillsTreasury Bills (TBills) are investment vehicles that allow investors to lend money to the government.read more, or simply the TBills

If the period is between 1 year to 10 years, one should use a Treasure Note.
 If the period is more than ten years, one can consider selecting Treasure Bond.
Examples of instruments with RiskFree Rates
The government of any country is assumed to have zero default riskDefault RiskDefault risk is a form of risk that measures the likelihood of not fulfillingÂ obligations, such as principal or interest repayment, and is determined mathematically based on prior commitments, financial conditions, market conditions, liquidity position, and current obligations, among other factors.read more as they can print money to pay back their debt obligation as required. Therefore, the interest rate on zerocoupon government securities like Treasury BondsTreasury BondsA Treasury Bond (or Tbond) is a government debt security with a fixed rate of return and relatively low risk, as issued by the US government. You can buy treasury bonds directly from the US Treasury or through a bank, broker, or mutual fund company.read more, Bills, and Notes, are generally treated as proxies for the riskfree rate of return.
Examples of RiskFree Rate of Return Formula (with Excel Template)
Letâ€™s see some simple to advanced examples to understand it better.
Example #1
Use the following data for the calculation of the riskfree rate of return.
 10 Year Government Bond Rate: 3.25%
 Inflation Rate: 0.90%
 Market Return: 6%
 Beta: 1.5
The riskfree rate of return can be calculated using the above formula as,
=(1+3.25%)/(1+0.90%)1
The answer will be –
Riskfree Rate of Return = 2.33%
The cost of equity can be calculated using the above formula as,
=2.33%+1.5*(6%2.33%)
Cost of Equity will be –
Cost of Equity = 7.84%
Example #2
Below is the information for India, for the year 2018
 Rate of Inflation: 4.74%
 10 Year Government Bond: 7.61%
The riskfree rate of return can be calculated using the above formula as,
=(1+7.61%)/(1+4.74%)1
The answer will be –
Riskfree Rate of Return = 2.74%
Applications
The rate of return in India for the government securities is much higher than the U.S. rates for the U.S. Treasury. It is factored by the growth rate of each economy and the stage of development at which each stands. Therefore, the investors are shifting and considering investing in Indian government securities and bonds. The availability of such securities is easily accessible as well.
The largely used models involving the riskfree rate are:
 Modern Portfolio Theory – Capital Asset Pricing Model
 Black Scholes Theory – Used for Stock Options and Sharpe RatioSharpe RatioSharpe Ratio, also known as Sharpe Measure, is a financial metric used to describe the investorsâ€™ excess return for the additional volatility experienced to hold a risky asset. You can calculate it by, Sharpe Ratio = {(Average Investment Rate of Return â€“ RiskFree Rate)/Standard Deviation of Investment Return} read more â€“ is a model used for the financial market dynamics containing derivative investment instruments.
The relevance of RiskFree Rate of Return Formula
It can be seen from the two perspectives: the business and the investors’ perspective. From an investor’s point of view, a rising riskfree rate of return signifies a stable government, a confident treasury, and, ultimately, the ability to expect high returns on one’s investment. On the other hand, a rising riskfree rate scenario can be problematic for businesses. The companies would have to now meet the investors’ expectations of higher returns by improving stock prices. It might turn stressful as the business would now have to show good projections and have to thrive on meeting these profitabilityProfitabilityProfitability refers to a company's abilityÂ to generate revenue and maximize profit above its expenditure and operational costs. It is measured using specific ratios such as gross profit margin, EBITDA, andÂ net profit margin. It aids investors in analyzingÂ the company's performance.read more projections.
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